Anna V. Ceguerra

Quantitative binomial distribution analyses of nanoscale like-solute atom clustering and segregation in atom probe tomography data

The applicability of the binomial frequency distribution is outlined for the analysis of the evolution nanoscale atomic clustering of dilute solute in an alloy subject to thermal ageing in 3D atom probe data. The conventional χ2 statistics and significance testing are demonstrated to be inappropriate for comparison of quantity of solute segregation present in two or more different sized system. Pearson coefficient, μ, is shown to normalize χ2 with respect to sample size over an order of magnitude. A simple computer simulation is implemented to investigate the binomial analysis and infer meaning in the measured value of μ over a series of systems at different solute concentrations and degree of clustering. The simulations replicate the form of experimental data and demonstrate the effect of detector efficiency to significantly underestimate the measured segregation. The binomial analysis is applied to experimental atom probe data sets and complementary simulations are used to interpret the results. Microsc. Res. Tech., 2008.

Crystallographic structural analysis in atom probe microscopy via 3D Hough transformation

Whereas the atom probe is regarded almost exclusively as a technique for 3D chemical microanalysis of solids with the highest chemical and spatial resolution, we demonstrate that the technique can be used for detailed crystallographic determinations. We present a new method for the quantitative determination of crystal structure (plane spacings and angles) using a Hough transformation of the reconstructed atom probe data. The resolving power is shown to be high enough to identify poorly established, discontinuous planes that are typical in semiconducting materials. We demonstrate the determination of crystal geometry around a grain boundary and the use of the technique for the optimisation of tomographic reconstruction. We propose that this method will enable automatic spatial analysis and, ultimately, automated tomographic reconstruction in atom probe microscopy.

Lattice rectification in atom probe tomography: toward true three-dimensional atomic microscopy

Atom probe tomography (APT) represents a significant step toward atomic resolution microscopy, analytically imaging individual atoms with highly accurate, though imperfect, chemical identity and three-dimensional (3D) positional information. Here, a technique to retrieve crystallographic information from raw APT data and restore the lattice-specific atomic configuration of the original specimen is presented. This lattice rectification technique has been applied to a pure metal, W, and then to the analysis of a multicomponent Al alloy. Significantly, the atoms are located to their true lattice sites not by an averaging, but by triangulation of each particular atom detected in the 3D atom-by-atom reconstruction. Lattice rectification of raw APT reconstruction provides unprecedented detail as to the fundamental solute hierarchy of the solid solution. Atomic clustering has been recognized as important in affecting alloy behavior, such as for the Al-1.1 Cu-1.7 Mg (at. %) investigated here, which exhibits a remarkable rapid hardening reaction during the early stages of aging, linked to clustering of solutes. The technique has enabled lattice-site and species-specific radial distribution functions, nearest-neighbor analyses, and short-range order parameters, and we demonstrate a characterization of solute-clustering with unmatched sensitivity and precision.

A three-dimensional Markov field approach for the analysis of atomic clustering in atom probe data

Solute clustering is increasingly recognised as a significant characteristic within certain material systems that can be tailored to the optimization of bulk properties and performance. Atom probe tomography (APT) is emerging as a powerful tool for the detection of these nanoscale features; however, complementary to experiment, precise and efficient characterization algorithms are required to identify and characterise these nanoclusters within the potentially massive three-dimensional atomistic APT datasets. In this study, a new three-dimensional Markov field (3DMF) cluster identification algorithm is proposed. The algorithm is based upon an analysis of the direct atomic neighbourhood surrounding each atom, and the only input parameter required utilises known crystallographic properties of the system. Further, an array of statistical approaches has been developed and applied with respect to the results generated by the 3DMF algorithm including: an S N statistic, a two-tailed z-test, a difference measure, the χ2 test, and a direct evaluation of the Warren–Cowley parameter for short-range ordering. Finally, the methodologies have been applied to the characterization of the nanostructural evolution of an Al-1.1Cu-0.5Mg (at.%) alloy subjected to a variety of heat treatments.

Atomically resolved tomography to directly inform simulations for structure–property relationships

Microscopy encompasses a wide variety of forms and scales. So too does the array of simulation techniques developed that correlate to and build upon microstructural information. Nevertheless, a true nexus between microscopy and atomistic simulations is lacking. Atom probe has emerged as a potential means of achieving this goal. Atom probe generates three-dimensional atomistic images in a format almost identical to many atomistic simulations. However, this data is imperfect, preventing input into computational algorithms to predict material properties. Here we describe a methodology to overcome these limitations, based on a hybrid data format, blending atom probe and predictive Monte Carlo simulations. We create atomically complete and lattice-bound models of material specimens. This hybrid data can then be used as direct input into density functional theory simulations to calculate local energetics and elastic properties. This research demonstrates the role that atom probe combined with theoretical approaches can play in modern materials engineering.

Integrating local and global features in automatic fingerprint verification

This paper presents a new approach for combining local and global recognition schemes for automatic fingerprint verification (AFV), by using matched local features as the reference axis for generating global features. In our specific implementation, minutia-based and shape-based techniques were combined. The first one matches local features (minutiae) by a point-pattern matching algorithm. The second one generates global features (shape signatures) by using the matched minutiae as its frame of reference. Shape signatures are then digitised to form a feature vector describing the fingerprint. Finally, a LVQ neural network was trained to match the fingerprints by using the difference of a pair of feature vectors. The experimental results show that the integrated system significantly outperforms the minutiae-based system in terms of classification accuracy and stability. This makes the new approach a promising solution for biometric applications.

Applying computational geometry techniques for advanced feature analysis in atom probe data

In this paper we present new methods for feature analysis in atom probe tomography data that have useful applications in materials characterisation. The analysis works on the principle of Voronoi subvolumes and piecewise linear approximations, and feature delineation based on the distance to the centre of mass of a subvolume (DCOM). Based on the coordinate systems defined by these approximations, two examples are shown of the new types of analyses that can be performed. The first is the analysis of line-like-objects (i.e. dislocations) using both proxigrams and line-excess plots. The second is interfacial excess mapping of an InGaAs quantum dot.

Quantitative dopant distributions in GaAs nanowires using atom probe tomography

Controllable doping of semiconductor nanowires is critical to realize their proposed applications, however precise and reliable characterization of dopant distributions remains challenging. In this article, we demonstrate an atomic-resolution three-dimensional elemental mapping of pristine semiconductor nanowires on growth substrates by using atom probe tomography to tackle this major challenge. This highly transferrable method is able to analyze the full diameter of a nanowire, with a depth resolution better than 0.17 nm thanks to an advanced reconstruction method exploiting the specimens crystallography, and an enhanced chemical sensitivity of better than 8-fold increase in the signal-to-noise ratio.

Short-range order in multicomponent materials.

The generalized multicomponent short-range order (GM-SRO) parameter has been adapted for the characterization of short-range order within the highly chemically and spatially resolved three-dimensional atomistic images provided by the microscopy technique of atom-probe tomography (APT). It is demonstrated that, despite the experimental limitations of APT, in many cases the GM-SRO results derived from APT data can provide a highly representative description of the atomic scale chemical arrangement in the original specimen. Further, based upon a target set of the GM-SRO parameters, measured from APT experiments, a Monte Carlo algorithm was utilized to simulate statistically equivalent atomistic systems which, unlike APT data, are complete and lattice based. The simulations replicate solute structures that are statistically consistent with other correlation measures such as solute cluster distributions, enable more quantitative characterization of nanostructural phenomena in the original specimen and, significantly, can be incorporated directly into other models and simulations.

Detecting and extracting clusters in atom probe data: A simple, automated method using Voronoi cells

The analysis of the formation of clusters in solid solutions is one of the most common uses of atom probe tomography. Here, we present a method where we use the Voronoi tessellation of the solute atoms and its geometric dual, the Delaunay triangulation to test for spatial/chemical randomness of the solid solution as well as extracting the clusters themselves. We show how the parameters necessary for cluster extraction can be determined automatically, i.e. without user interaction, making it an ideal tool for the screening of datasets and the pre-filtering of structures for other spatial analysis techniques. Since the Voronoi volumes are closely related to atomic concentrations, the parameters resulting from this analysis can also be used for other concentration based methods such as iso-surfaces.